Problem 13-24 Simple Rate of Return; Payback Period; Internal Rate of Return [LO13-1, LO13-3, LO13-6]

The Elberta Fruit Farm of Ontario always has hired transient workers to pick its annual cherry crop. Janessa Wright, the farm manager, just received information on a cherry picking machine that is being purchased by many fruit farms. The machine is a motorized device that shakes the cherry tree, causing the cherries to fall onto plastic tarps that funnel the cherries into bins. Ms. Wright has gathered the following information to decide whether a cherry picker would be a profitable investment for the Elberta Fruit Farm:

1. Currently, the farm is paying an average of $200,000 per year to transient workers to pick the cherries.
2. The cherry picker would cost $250,000. It would be depreciated using the straight-line method and it would have no salvage value at the end of its 8-year useful life.
3. Annual out-of-pocket costs associated with the cherry picker would be: cost of an operator and an assistant, $98,000; insurance, $5,000; fuel, $15,000; and a maintenance contract, $20,000.

Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor using tables.

Required:

1. Determine the annual savings in cash operating costs that would be realized if the cherry picker were purchased.

2a. Compute the simple rate of return expected from the cherry picker.

2b. Would the cherry picker be purchased if Elberta Fruit Farms required rate of return is 18%?

3a. Compute the payback period on the cherry picker.

3b. The Elberta Fruit Farm will not purchase equipment unless it has a payback period of five years or less. Would the cherry picker be purchased?

4a. Compute the internal rate of return promised by the cherry picker.

4b. Based on this computation, does it appear that the simple rate of return is an accurate guide in investment decisions?

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0.126 0.116 0.107 0.317 0287 0261 O 237 0.215 0.195 0.178 0162 0148 0 135 0, 123 O. 112 . 103 O004 0086 10 0.676 0614 0558 0.5oe 0.463 0422 0.386 0.352 0.322 0295 0.270 0.247 0227 o 12 0.625 0557 0.497 0444 0.397 O 356 0319 0286 0257 0.231 0208 O 187 168 0 152 0 137 0124 O 13 0.601 0530 0469 0 415 0368 0326 0.290 0258 0229 0204 O 182 O 163 O 145 030 0116 a,04 14 0577 0505 0442 0.388 0 15 0.555 0.481 0417 0.362 0.315 0.275 0.239 0.209 0.183 0.160 0.140 0123 0108 0.095 0084 16 0.534 0.458 0.394 0.339 0.292 17 0513 0436 0.371 0.317 0.270 0.231 0.198 0.170 o0.146 0.125 0.108 0.093 0080 0.069 0060 18 0.494 0.416 0.350 0.296 0.250 0212 0.180 0.153 0.130 0.111 0.095 0081 0069 0.059 0.340 0.299 0.263 0055 0.049 0.044 0074 0065 0.057 0.051 0045 0040 0035 0.218 0188 0.163 0.141 0.123 0,107 0093 0081 0071 0.062 0054 0.047 0042 0036 0032 0028 0.232 0.205 0.181 0.160 0.141 0.125 0111 0.099 0.088 0.078 0.069 0.062 0.083 0.07o 0060 0.051 0.043 0.037 0031 0.027 0.023 0020 0017 20 0.456 0.377 0.3 12 0.258 0.215 0.178 0.149 0.124 0.104 0087 0.073 0.061 0051 0.043 0.037 0031 0026 0.022 0019 0016 0.014 0.012 21 0439 0359 0.294 0242 0.199 o.164 0.135 0.112 0093 0077 0064 0.053 0044 0037 0031 0.026 0.022 0018 0015 0013 0011 0.009 0046 0038 0032 0.026 0.022 0018 0015 0.013 0011 0009 0.007 0033 0027 0022 0.018 0015 0012 0010 0.009 0007 0.006 008 0.007 0006 0.o05 0010 0009 0.007 0.006 0.005 0004 24 0390 0.310 0247 0.197 0.158 0.126 0.102 0082 0066 0053 0043 0035 0028 0023 0019 0015 0013 001o o 25 0.375 0.295 0.233 0.184 0.146 0116 0092 0.074 0.059 0047 0038 0030 0024 0020 0016 0013 26 0.361 0.281 0.220 0172 0.135 0.106 0.084 0.066 0.053 0042 0.033 0026 0021 0017 0014 0011 0009 0.007 0006 000s 0014 0011 0.009 0.007 0.006 0.005 0004 0003 0.002 30 0308 0.231 0.174 0.131 0.099 0.075 0057 0.044 0033 0026 0020 0.015 0012 0009 0.007 0.005 0004 40 0208 0.142 0.097 0067 0.046 0032 0022 0015 0011 0008 0.005 0.004 0.003 0002 0.001 0.001 0001 0000 0000 0.000 0000 0.000 0.003 0.003 0002 0.002 0.001 1 Present Value of an Anity of S1nArrears,1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 1 0.962 0952 0943 0935 0.926 0917 0.909 0.901 0893 0.885 0.877 0.870 0.862 0855 0.847 0.840 0.833 0.826 0820 0.813 0.806 0.800 1.886 1859 1833 1.808 1.783 1.759 1.736 1.713 1.690 1668 1647 1626 1.605 1.585 1.566 1547 1528 1.509 1.492 1.474 1.457 1.440 2.775 2.723 2673 2.624 2.577 2.531 2.487 2444 2.402 2.361 2.322 2283 2246 2210 2.174 2.140 2.106 2074 2042 2011 1.981 1.952 4 3.630 3546 3.465 3.387 3312 3.240 3.170 3.102 3037 2974 2914 2855 2.798 2743 2.690 2639 2589 2540 2.494 2448 2404 2362 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3605 3517 3433 3352 3.274 3.199 3.127 3058 2.991 2926 2864 2803 2745 2689 6 5.242 5076 4917 4767 4.623 4.486 4.355 4.231 4.111 3998 3889 3.784 368S 3589 3.498 3410 3326 3245 3.167 3092 3020 2951 6.002 5.786 5582 5.389 5.206 5033 4.868 4.712 4564 4.423 4288 4.160 4.039 3922 3.812 3706 3.605 3.508 3.416 3.327 3.242 3.161 6.733 6463 6210 5.971 5747 5535 5.335 5.146 4968 4799 4639 4487 4.344 4 207 4.078 3.954 3.837 3.726 3.619 3518 3.421 3.329 9 7.435 7 10 6.802 6.515 6.247 5.995 5759 5.53 5.328 5132 4946 4772 4 607 4 451 4 303 4163 4031 3.905 3.786 3.673 3566 3463 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.426 5216 5019 4833 4.659 4.494 4.339 4192 4.054 3.923 3.799 3682 3.571 11 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5938 5687 5453 5234 5029 4836 4.656 4486 4.327 4.177 4.035 3902 3.776 3656 9385 8.863 8.384 7.943 7536 7.161 6.814 6.492 6. 194 5918 5660 5421 5.197 4988 4.793 4611 4439 4.278 4127 3.985 3.851 3.725 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6424 6.122 5.842 5583 5.342 5.118 4910 4715 4533 4.362 4.203 4.053 3.912 3.780 14 10.563 9899 9.295 8.745 8244 7.786 7.367 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4802 4611 4.432 4.265 4.108 3962 3824 15 11.118 10.380 9.712 9.108 8559 8.061 7.606 7.191 6.811 6462 6142 5.847 5575 5.324 5.092 4.876 4.675 4.489 4.315 4.153 4.001 3859 16 11.652 10.838 10.106 9.447 8851 8.313 7.824 7.379 6974 6604 6265 5.954 5.668 5.405 5.162 4938 4.730 4536 4.357 4.189 17 12166 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120 6.729 6373 6.047 5.749 5.475 5.222 4.990 4775 4.576 4.391 4.219 18 12.659 11.690 10.828 10.059 9372 8.756 8.201 7.702 7250 6840 6467 6.128 5.818 5534 5.273 5.033 4.812 4.608 4419 4.243 4080 3.928 19 13.134 12.085 11.158 10.336 9604 8.950 8.365 7.839 7 366 6938 6550 6.198 5.877 5584 5.316 5070 4.843 4.635 4.442 4.263 4.097 3.942 20 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7963 7469 7025 6623 6.259 5.929 5.628 5.353 5101 4870 4.657 4.460 4.279 4.110 3954 21 14.029 12.821 11.764 10.836 10.017 9.292 8.649 8.075 7562 7.102 6687 6.312 5.973 5.665 5.384 5.127 4891 4675 4.476 4.292 4.121 3.963 22 14.451 13.163 12042 11.061 10.201 9.442 8772 8.176 7645 7.170 6743 6.359 6011 5.696 5410 5.149 4909 4.690 4.488 4.302 4.130 3970 23 14.857 13489 12 303 11.272 10.371 9.580 8883 8.266 7718 7230 6792 6399 6044 5723 5432 5.167 4925 4.703 4499 4.311 4.137 3976 24 15.247 13799 12.550 11.469 10529 9.707 8.985 8 348 7.784 7 283 6835 6434 6073 5746 5.451 5.182 4937 4.713 4507 4.318 4.143 3981 25 15.622 14094 12.783 11654 10 675 9.823 9.077 8.422 7 843 7330 6873 6464 6097 5766 5.467 5.195 4.948 4.721 4514 4323 4.147 3 985 26 15.983 14.375 13.003 11.826 10810 9.929 9161 8.488 7896 7 372 6906 6.491 6118 5783 5.480 5206 4956 4728 4.520 4328 4.151 3988 27 16.330 14 643 13.211 11987 10935 10.027 9.237 8.548 7943 7409 6935 6514 6.136 5.798 5.492 5215 4964 4.734 4524 4.332 4.154 3990 28 16663 14.898 13.406 12.137 11.051 10 116 9.307 8.602 7984 7441 6961 6.534 6.152 5.810 5502 5223 4 970 4739 4 528 4.335 4 157 3992 29 16984 15.141 13.591 12 278 11.158 10.198 9.370 8.650 8.022 7.470 6983 6.551 6 166 5820 5 510 5229 4.975 4743 4531 4.337 4.159 3994 30 17.292 15.372 13.765 12.409 11.258 10.274 9427 8694 8055 7496 7003 6566 6 177 5.829 5517 5235 4979 4.746 4 534 4.339 4.160 3995 40 19.793 17.159 15.046 13.332 11925 10.757 9.779 8951 8 244 7634 7105 6.642 6233 5.871 5.548 5.258 4997 4760 4544 4 347 4.166 3999